The Glass Crystal

Crystals conduct heat well because their periodic structure supports long-range phonon transport. Glasses conduct heat poorly because their disordered structure scatters phonons at every length scale. This dichotomy — crystal versus glass, order versus disorder — maps directly to thermal conductivity: crystals are high, glasses are low, and the structural reason is clear.

Re₆Se₈Te₇ and Re₆Te₁₅ are crystalline. X-ray diffraction confirms long-range order. The atoms sit on well-defined lattice sites. The structure is periodic. But their thermal conductivities — 0.32 and 0.53 W m⁻¹ K⁻¹ — are among the lowest measured in any inorganic bulk crystal, rivaling amorphous materials (arXiv:2603.28267, March 2026).

The mechanism: hierarchical bonding. These are superatomic compounds — materials built from rigid molecular clusters (Re₆Se₈ or Re₆Te₈ units) connected to each other through soft tellurium networks. Within each cluster, the rhenium-chalcogenide bonds are stiff and the atoms vibrate coherently. Between clusters, the tellurium bridges are floppy. The phonon spectrum splits: high-frequency modes propagate within clusters (local, confined), while low-frequency modes that should carry heat between clusters are disrupted by the soft links.

The evidence for glass-like phonon behavior in a crystal: a large Grüneisen parameter (1.93, indicating strong anharmonicity), sound speeds below 1,482 m/s (slower than sound in water), and a boson peak — the excess density of low-energy vibrational states that is the hallmark of glasses and has no counterpart in clean crystals. Above 350 K, the thermal conductivity approaches the theoretical glass limit calculated from diffusion models.

The structural insight: order and disorder can occupy different levels of the same material simultaneously. The crystal is ordered at the scale of the lattice — cluster positions repeat periodically. The phonon transport is disordered at the scale of the inter-cluster connections — the soft tellurium network scatters heat as effectively as structural randomness would. The crystal doesn't need to be disordered to act like a glass. It needs the bonds that carry heat to be weaker than the bonds that define the structure. The hierarchy does what disorder does.